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The Dynamic Complexity of Acyclic Hypergraph Homomorphisms,show that an answer to this problem can be maintained under single-edge changes of ., as long as it stays acyclic, in the . framework of Patnaik and Immerman that uses updates expressed in first-order logic. If additionally also changes of . are allowed, we show that it is unlikely that existence of homomorphisms can be maintained in ..

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,On the Parameterized Complexity of the Connected Flow and Many Visits?TSP Problem,the capacities and induces a (strongly) connected subgraph. This generalizes previously studied problems like the ...We study the parameterized complexity of . parameterized by |.|, the treewidth . and by vertex cover size . of . and provide: .To achieve some of our results, we significantly extend an approach by Kowalik et al.?[ESA’20].

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https://doi.org/10.1007/978-3-211-99699-7or finding separators, a separator minimization method for a refinement of found separators, and a refinement of an obtained treedepth decomposition by merging techniques of tree rotations. This approach enables us to quickly obtain low-depth decompositions of very large graphs.

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Barbara Ann Hamkalo,John Papaconstantinounential Time Hypothesis, we show there is no .-time algorithm for . even when restricted to .-vertex bipartite graphs, and also show that . can be solved in . time by means of an exact branching algorithm.

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